let I be Program of SCM+FSA; :: thesis: ( I is InitClosed & I is good implies I is keepInt0_1 )
assume A1: ( I is InitClosed & I is good ) ; :: thesis: I is keepInt0_1
then A2: not I destroys intloc 0 by SCMFSA7B:def 5;

now

let s be State of SCM+FSA; :: thesis: ( Initialize ((intloc 0) .--> 1) c= s implies for p being the Instructions of SCM+FSA -valued ManySortedSet of NAT st I c= p holds
for k being Element of NAT holds (Comput (p,s,k)) . (intloc 0) = 1 )
assume A3: Initialize ((intloc 0) .--> 1) c= s ; :: thesis: for p being the Instructions of SCM+FSA -valued ManySortedSet of NAT st I c= p holds
for k being Element of NAT holds (Comput (p,s,k)) . (intloc 0) = 1
let p be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: ( I c= p implies for k being Element of NAT holds (Comput (p,s,k)) . (intloc 0) = 1 )
assume A4: I c= p ; :: thesis: for k being Element of NAT holds (Comput (p,s,k)) . (intloc 0) = 1
let k be Element of NAT ; :: thesis: (Comput (p,s,k)) . (intloc 0) = 1
thus (Comput (p,s,k)) . (intloc 0) = s . (intloc 0) by A2, A3, Th37, A1, Th35, A4
.= 1 by A3, Th7 ; :: thesis: verum

end;

hence I is keepInt0_1 by Def3; :: thesis: verum